Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2017 Grade 5 Algebra
Problem
Solution
1) Aaron is making a pattern with tiles.
If he keeps this pattern going, how many tiles will be in figure 20?
1. Write out in a list the number of tiles in each figure:
    5   8   11
2. Determine the increment between each figure = 3 tiles.
3. Choose one of these solutions:
Method 1: list the elements
Write out all the elements up to the one you want using the increment you found:
5 8 11 14 17 20 23 26 29 32 35 38 41 44 47 50 53 56 59 62 		Method 2: Use the formula for an arithmetic sequence:
AN = A1 + D x (N - 1) where:
A1 is the first term, = 5
AN is the Nth term
(the term you are looking for), and
D is the number that is added to each term.
A20 = 5 + 3 x (20-1) = 5 + 57 = 62
2) It costs a fixed fee to set up a party at the local trampoline gym. After that amount is paid, there is a cost per guest. Based on the table below, how much is the fixed fee to set up a party?
1. The number of added guests in the second column is 9 - 5 = 4.
2. The increase in cost from the first column to the second is $35
3. The added cost per guest = $35/4 = $8.75
4. Multiply the number of guests in the first column by this added cost per guest =
    5 x $8.75 = $43.75
5. Subtract this from the first column to get the fixed cost =
    $59 - $43.75 = $15.25

Problem
Solution

3) A pile of 30 coins is worth $5.00. There are only quarters, dimes, and nickels in the pile. There are only 2 dimes. How many quarters are there?		 1. Subtract from the total worth of the pile the 2 dimes = $4.80
This is the amount of money that is in quarters and nickels.
2. There are now 28 coins that are quarters or nickels.
3. This is now a guess-and-check problem. Here's the table:
Guess ## quarters# nickelsTotal
$
11711$4.80
There are 17 quarters.

4) I'm thinking of a number. If I multiply my number by 12 and then add 2, I get the same result as if I had added 90 to my number. What is my number? 		Using N for the number,
1. Write the expression for
    "multiply my number by 12 and then add 2" = 12N + 2.
2. Write the expression for "add 90 to my number" = 90 + N.
3. Set these two expressions equal to each other and solve.
    12N + 2 = 90 + N
    11N = 88
    N = 8
5) Raihana is reading a new book. She just finished 1/3 of the book. She notices that if she reads 60 more pages she will be 1/2 done with the book. How many pages long is the book? 1. The difference between 1/2 and 1/3 of the book is 1/6 of the book.
2. If that fraction is 60 pages then the total book is 360 pages.